Decoding rank metric Reed-Muller codes
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911285587738624 |
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| author | Couvreur, Alain Pratihar, Rakhi |
| author_facet | Couvreur, Alain Pratihar, Rakhi |
| contents | In this article, we investigate the decoding of the rank metric Reed--Muller codes introduced by Augot, Couvreur, Lavauzelle and Neri in 2021. These codes are defined from Abelian Galois extensions extending the construction of Gabidulin codes over arbitrary cyclic Galois extensions. We propose a polynomial time algorithm that rests on the structure of Dickson matrices, works on any such code and corrects any error of rank up to half the minimum distance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_04766 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Decoding rank metric Reed-Muller codes Couvreur, Alain Pratihar, Rakhi Information Theory Combinatorics In this article, we investigate the decoding of the rank metric Reed--Muller codes introduced by Augot, Couvreur, Lavauzelle and Neri in 2021. These codes are defined from Abelian Galois extensions extending the construction of Gabidulin codes over arbitrary cyclic Galois extensions. We propose a polynomial time algorithm that rests on the structure of Dickson matrices, works on any such code and corrects any error of rank up to half the minimum distance. |
| title | Decoding rank metric Reed-Muller codes |
| topic | Information Theory Combinatorics |
| url | https://arxiv.org/abs/2501.04766 |